Question

Bhatya invested 800 on simple interest of rate 5%
per annum . How many years will it take his money to
reach * 1000 ?
(A) 4 years (B) 5 years
(C) 2 years
(D) 20 years​

Answer 1

➤ Given :-

Principle :- ₹800

Rate of interest :- 5%

Total Amount :- ₹1000

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➤ To Find :-

The time taken to receive the money back...

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★ How to do :-

Here, we are given with the principle amount, the rate of interest and the total amount received back at end of the time period. But, we are not given with the time taken to receive the money back from the bank. We are asked to find the same. We have an appropriate formula to calculate the time period of this investment by which we can easily find the answer. But, we need the interest amount for finding that. So, first we should find the simple interest and then, we can solve for time. So, let's solve!!

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➤ Solution :-

Simple Interest :-

${\sf \leadsto \underline{\boxed{\sf Total \: Amount - Principle}}}$

Substitute the given values.

${\tt \leadsto 1000 - 800}$

Subtract the values to get the interest amount.

${\tt \leadsto Rs \: \: 200}$

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Now, let's find the time period of the investment.

Time :-

${\sf \leadsto \underline{\boxed{\sf \dfrac{SI \times 100}{P \times R}}}}$

Substitute the given values.

${\tt \leadsto \dfrac{200 \times 100}{800 \times 5}}$

Write the numerator and denominator in lowest form by cancellation method.

${\tt \leadsto \dfrac{\cancel{200} \times 100}{\cancel{800} \times 5} = \dfrac{1 \times 100}{4 \times 5}}$

Multiply the remaining numbers on numerator and denominator.

${\tt \leadsto \cancel \dfrac{100}{20} = 5 \: years}$

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${\red{\underline{\boxed{\bf So, \: option - (B) \: is \: the \: correct \: answer}}}}$

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$\dashrightarrow$ Some related formulas :-

$\begin{gathered} \small \boxed{\begin{array} {cc} \large \dag \: \sf More \: formulas \\ \\ \sf \bigstar \: Simple \: interest = \dfrac{P \times R \times T}{100} \\ \\ \sf \bigstar \: Principle = \dfrac{SI \times 100}{R \times T} \\ \\ \sf \bigstar \: Rate \: of \: interest = \dfrac{SI \times 100}{P \times T} \\ \\ \sf \bigstar \: Time = \dfrac{SI \times 100}{P \times R} \end{array}} \end{gathered}$

Answer 2

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$\large{ \underline{ \orange{ \bf{Answer}}}}$

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$\bf \green{Given \: –}$

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• Total amount = Rs.1000
• Principal = Rs.800
• Rate of interest = 5%

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$\bf \green{To \: Find \: – }$

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• How much years will it take his money to reach Rs.1000.

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$\large{ \underline{ \bf{ \orange{Solution}}}}$

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Simple Interest :—

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$: \rightarrow \tt{total \: amount \: - \: principle}$

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$: \rightarrow1000 - 800$

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$: \rightarrow200$

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Time :—

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$\begin{gathered}{ \bf{ \red{ \frac{SI \times 100}{ P \times R } }}} \end{gathered}$

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$\implies \sf{ \dfrac{\cancel{200} \times 100}{\cancel{800} \times 5} }$

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$\implies \sf{ \dfrac{1 \times 100}{4 \times 5} }$

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$\implies \cancel{ \dfrac{100}{20} }$

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$\implies \sf{5 \: yrs}$

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$\begin{gathered}{ \underline{ \boxed{ \sf{ \blue{Therefore, option \: B \: is \: correct}}}}} \end{gathered}$

$\: \: \\ \:$

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